What it means
Suppose a company must choose between two machines. One lasts three years and the other lasts six, and each has a positive NPV.
Comparing the two NPVs directly would be unfair, because the shorter machine's benefits stop after three years while the longer machine keeps going. The replacement chain method fixes this by repeating the shorter project until it matches the length of the longer one, or the lowest common multiple of the two lives.
For machines lasting three and six years, the three-year machine is bought twice. The NPV of the second purchase is discounted back to today, because it happens three years later.
The total NPV of the chain is then compared with the NPV of the longer project. The option with the higher chain NPV is better, provided the assumptions hold.
These assumptions are that the projects can be repeated on the same terms, that the cost of capital stays the same, and that the company needs the service for the whole period. An alternative approach, the equivalent annual annuity method, converts each NPV into a yearly figure and avoids the need to repeat projects.
Both methods give the same ranking when assumptions are consistent. The chain method is more intuitive for non-finance managers, but can become unwieldy when lives are, for example, 7 and 11 years.
Finance teams should remember that real-world replacements rarely match the original. Technology may improve, prices may change, and the business may not need the asset after a few years.
The method gives a disciplined comparison, but its results are only as reliable as the repeat assumption.
In practice
Real-world examples.
Example
A delivery firm compares a van that lasts four years with a larger vehicle that lasts eight years. It repeats the cheaper van twice to cover eight years and discounts the second purchase back to today. The comparison shows the vans are slightly better, so the firm buys the smaller one.
Example
A hospital chooses between two scanners, one with a five-year life and the other with ten years. The finance team builds a chain of two five-year scanners and compares its NPV with the ten-year model. The longer-lasting scanner wins because it has lower maintenance costs.
Example
A restaurant group decides between two kitchen systems with lives of three and four years. The common timeline is 12 years, so it assumes four cycles of the first and three of the second. The analyst notes the long horizon makes the result less certain, and also calculates the equivalent annual annuity as a cross-check.
Formula
Calculation
NPV of chain = NPV of first cycle + NPV of repeat / (1 + r)^n + further repeats discounted in the same way
Suppose machine A lasts 3 years and has an NPV of $12,000. Machine B lasts 6 years and has an NPV of $20,000. The cost of capital is 10%. Chain NPV for A over 6 years = 12,000 + 12,000 / (1.10)^3 = 12,000 + 12,000 / 1.331 = 12,000 + 9,015.78 = $21,015.78. Machine A's chain NPV of $21,015.78 is higher than Machine B's $20,000, so A is the better choice, despite its lower single-cycle NPV.Case study
Seen in the real world.
Northfield Printing is an illustrative, fictional company choosing between two printing presses. Press X costs less and lasts three years, while Press Y costs more and lasts six years.
The single-cycle NPVs were $12,000 for Press X and $20,000 for Press Y, which led the production manager to favour Press Y. The finance analyst built a six-year chain for Press X using a 10% discount rate and found a chain NPV of about $21,016.
On that basis, Press X was slightly better, but the analyst warned that the result depended on being able to buy an identical press in three years at the same price. The board chose Press X with a review point at year three, and the illustrative lesson was that comparing unequal lives requires a like-for-like timeline.
Watch out
Common mistakes.
- Comparing the NPVs of projects with different lives directly, which favours the longer project.
- Forgetting to discount the later cycles back to today, which overstates the value of repeating the project.
- Assuming that replacement costs and cash flows will be identical in future cycles, when prices and technology can change.
Questions
People also ask.
When should I use the replacement chain method?
Use it when you must choose between mutually exclusive projects with unequal lives and the company expects to need the service over the longer period.
How does it differ from the equivalent annual annuity?
The chain method repeats projects over a common timeline, while the annuity method converts each NPV to an annual figure, and both normally give the same ranking.
What if the common timeline is very long?
Choose the equivalent annual annuity method, since repeating projects over many decades is impractical and adds uncertainty.
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